7,986 research outputs found
Soliton dynamics in damped and forced Boussinesq equations
We investigate the dynamics of a lattice soliton on a monatomic chain in the
presence of damping and external forces. We consider Stokes and hydrodynamical
damping. In the quasi-continuum limit the discrete system leads to a damped and
forced Boussinesq equation. By using a multiple-scale perturbation expansion up
to second order in the framework of the quasi-continuum approach we derive a
general expression for the first-order velocity correction which improves
previous results. We compare the soliton position and shape predicted by the
theory with simulations carried out on the level of the monatomic chain system
as well as on the level of the quasi-continuum limit system. For this purpose
we restrict ourselves to specific examples, namely potentials with cubic and
quartic anharmonicities as well as the truncated Morse potential, without
taking into account external forces. For both types of damping we find a good
agreement with the numerical simulations both for the soliton position and for
the tail which appears at the rear of the soliton. Moreover we clarify why the
quasi-continuum approximation is better in the hydrodynamical damping case than
in the Stokes damping case
Loop space and evolution of the light-like Wilson polygons
We address a connection between the energy evolution of the polygonal
light-like Wilson exponentials and the geometry of the loop space with the
gauge invariant Wilson loops of a variety of shapes being the fundamental
degrees of freedom. The renormalization properties and the differential area
evolution of these Wilson polygons are studied by making use of the universal
Schwinger quantum dynamical approach. We discuss the appropriateness of the
dynamical differential equations in the loop space to the study of the energy
evolution of the collinear and transverse-momentum dependent parton
distribution functions.Comment: 8 pages, 2 eps figures; needs ws-ijmpcs.cls (supplied). Invited talk
presented at the QCD Evolution Workshop, May 14 - 17 (2012), Thomas Jefferson
National Accelerator Facility, Newport News (VA), US
Long-range effects on superdiffusive solitons in anharmonic chains
Studies on thermal diffusion of lattice solitons in Fermi-Pasta-Ulam
(FPU)-like lattices were recently generalized to the case of dispersive
long-range interactions (LRI) of the Kac-Baker form. The position variance of
the soliton shows a stronger than linear time-dependence (superdiffusion) as
found earlier for lattice solitons on FPU chains with nearest neighbour
interactions (NNI). In contrast to the NNI case where the position variance at
moderate soliton velocities has a considerable linear time-dependence (normal
diffusion), the solitons with LRI are dominated by a superdiffusive mechanism
where the position variance mainly depends quadratic and cubic on time. Since
the superdiffusion seems to be generic for nontopological solitons, we want to
illuminate the role of the soliton shape on the superdiffusive mechanism.
Therefore, we concentrate on a FPU-like lattice with a certain class of
power-law long-range interactions where the solitons have algebraic tails
instead of exponential tails in the case of FPU-type interactions (with or
without Kac-Baker LRI). A collective variable (CV) approach in the continuum
approximation of the system leads to stochastic integro-differential equations
which can be reduced to Langevin-type equations for the CV position and width.
We are able to derive an analytical result for the soliton diffusion which
agrees well with the simulations of the discrete system. Despite of
structurally similar Langevin systems for the two soliton types, the algebraic
solitons reach the superdiffusive long-time limit with a characteristic
time-dependence much faster than exponential solitons. The soliton
shape determines the diffusion constant in the long-time limit that is
approximately a factor of smaller for algebraic solitons.Comment: 7 figure
Evolution and Dynamics of Cusped Light-Like Wilson Loops in Loop Space
We discuss the possible relation between the singular structure of TMDs on
the light-cone and the geometrical behaviour of rectangular Wilson loops.Comment: Proceedings for Diffraction 2012, Lanzarote, Spain. 5 pages, 2
figure
Cusped light-like Wilson loops in gauge theories
We propose and discuss a new approach to the analysis of the correlation
functions which contain light-like Wilson lines or loops, the latter being
cusped in addition. The objects of interest are therefore the light-like Wilson
null-polygons, the soft factors of the parton distribution and fragmentation
functions, high-energy scattering amplitudes in the eikonal approximation,
gravitational Wilson lines, etc. Our method is based on a generalization of the
universal quantum dynamical principle by J. Schwinger and allows one to take
care of extra singularities emerging due to light-like or semi-light-like
cusps. We show that such Wilson loops obey a differential equation which
connects the area variations and renormalization group behavior of those
objects and discuss the possible relation between geometrical structure of the
loop space and area evolution of the light-like cusped Wilson loops.Comment: Invited mini-review article to Physics of Particles and Nuclei. 16
pages, 9 eps figures; v2: references style changed, citations corrected and
update
Scattering of vortex pairs in 2D easy-plane ferromagnets
Vortex-antivortex pairs in 2D easy-plane ferromagnets have characteristics of
solitons in two dimensions. We investigate numerically and analytically the
dynamics of such vortex pairs. In particular we simulate numerically the
head-on collision of two pairs with different velocities for a wide range of
the total linear momentum of the system. If the momentum difference of the two
pairs is small, the vortices exchange partners, scatter at an angle depending
on this difference, and form two new identical pairs. If it is large, the pairs
pass through each other without losing their identity. We also study head-tail
collisions. Two identical pairs moving in the same direction are bound into a
moving quadrupole in which the two vortices as well as the two antivortices
rotate around each other. We study the scattering processes also analytically
in the frame of a collective variable theory, where the equations of motion for
a system of four vortices constitute an integrable system. The features of the
different collision scenarios are fully reproduced by the theory. We finally
compare some aspects of the present soliton scattering with the corresponding
situation in one dimension.Comment: 13 pages (RevTeX), 8 figure
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